Solution of triangles Questions and Answers

1 Find the sine cosine and tangent of angle in the triangle below Leave answers in simplified fraction form 3 pts C 17 15 8

Every spring Lowland High School administers a standardized test that includes only math and science questions at various levels of difficulty On the standardized test approximately 6 percent of the math questions and 9 percent of the science questions are categorized as very difficult questions If the test included 153 math questions and 267 science questions which of the following is the closest to the total number of very difficult questions on this standardized test A 9 3 17 C 24 33

A person is waiting to hear a certain song on the radio to try to win a contest for concert tickets The radio station manager promises that they will play the song randomly once sometime between 5 00pm and 10 00pm The person had to work and do some chores and was only able to listen to the radio from 6 00pm to 7 30pm What is the probability that the person heard the song during the time they listened 26 30 32 36

Mrs Jones asked her students what type of smart phones her students had owned over the last 3 years and created a VENN diagram to display that data Android iPhone COD How many of the students owned an Android phone OR an iPhone 5 12

Given P A 0 S P B 0 4 P A or B 0 7 determine the probability of P A and B if the two events are inclusive use either of the diagrams below to help you P Q PO 70 0 20 0 30 0 50 0 90 PLO

Solve the equation where x is any real number cos2x 1 2

The function g x 1 1 x 41 8 models the median height g x in inches of children who are x months of age The graph of g is shown 50 40 30 20 10 04 0 1020 30 405060 23 COLAR a Describe how the graph can be obtained using transformations of the square root function f x x OA Shrink f x horizontally by a factor of 1 1 Shift f x down by 41 8 units OB Stretch f x vertically by a factor of 1 1 Shift f x right by 41 8 units OC Stretch f x horizontally by a factor of 1 1 Shift f x right by 41 8 units OD Stretch f x vertically by a factor of 1 1 Shift f x up by 41 8 units

A B C and D are constants then which of the followrig statements is true about the graph of y A cos Bx C D Choose the correct answer OA The range is A D JA DI OB The range is A D IA DI OC The range is OD The range is A D JA D

Use a graphing utility to approximate to three decimal places the solutions of the equation in the interval 0 2TT Enter your answers as a comma separated list 3 sin x 2 0

3 6 Find X Found 2 decimal 3 H 12 X

6 In right triangle ABC shown in the diagram below altitude AD is drawn to hypotenuse AC DB 5 and BC 20 What is the length of the altitude in simplest radical form Method B A D Work

5 Find the angle labeled 0 12 m 0 150 m 0 Method Work

In AGEF G is a right angle and FG EG If FG To got add of hu 10 what is the length of EF in simplest radical form is to and admi

8 Find the value of x F X A 4 m 40 7 m Method Work

6 In right triangle ABC below AC 9 What is the length of AB Method a 4 5 b 3 3 c 6 3 d 18 Work A 60

10 In rectangle ABCD below mzDAC 35 If AB Method Work 6 determine the length of AD to the nearest tenth A Atita B

11 5m 5m 11 5 m 1 Cheila is incorrect One of the cylinders is tilted 10m 12 m Sheila believes that the two cylinders shown in the diagram below have equal volumes Is Sheila correct or incorrect Select ALL that apply Sheila is incorrect The volumes of both cylinders are not equal Select all correct options MSQ Sheila is correct Using Cavalieri s Principle and the formula v Bh or V 2h proves the volumes of the cylinders are equal Sheila is correct Both cylinders radii and height are equal so their volumes are the same 5 Sheila is correct When two cylinders have the same base areas and the same height their volumes must be the same

A B ABCA ADEF AABC AEFD C The triangles shown are similar Which is an appropriate similarity statem C ACBA AEFD 3 A E 1

Find the area of the triangle below Be sure to include the correct unit in your answer If necessary refer to the list of geometry formulas O 24 cm 26 cm 10 cm cm cm cm

When I bought my TV it said it was a 75 inch TV That is the measure of the diagonal of the television The height of the television is 29 6 inches What is the lenght of the TV rounded to the nearest tenth of an inch

1 mLH 26 H 4 m2R RM 68 6 use your new conjectures to find the missing measures 2 mLG 35 cm R 7 m2T 78 M perimeter of ATBS 2 y 22 5 cm 38 5 cm 24 B 5 m2Y RD 3 5 cm 28 8 The perimeter of ANBC is 555 m NB mAN 2x 90 m 3 LOLE 2 mZD m2U MD 6 The perimeter of AMUD is 36 6 cm 14 cm 35 285 in for Exercises 16 9 The perimeter of AMTV is 605 in MV mZM x 99

Find the exact values for the six trigonometric functions of the angle 0 sin 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators cos 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators tan 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators sec 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators csc 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators cot 8 Simplify your answer including any radicals Use integers or fractions for 60 11

Lines and s are cut by a transversal for 143 3x 14 What value for proves that r s Type your answer

Each of the functions in the left column i iv differs by a constant from one of the functions in th right column a d Match the functions by finding the constant by which they differ and using a Pythagorean identity to verify your answers b i f x 4 sin x ii f x 2 cos x 2 sin x 1 iii f x 3 sin x 2 cos x iv f x sin x cos x 2 sin x cos x a g x b g x 4 sin x c g x 2 sin x 2 cos x d g x sin x 5 sin x 12 cos x

Find the value of x 47 58

For the right triangles below find the exact values of the side lengths a and d If necessary write your responses in simplified radical form 45 5 45 a 60 4 30 d a d 0 3 X

4 Sketch the graph of the function f 0 0 1 t 2 and determine whether it is of exponential order and f t f t 2 for t 2 2

Find an equation for the graph sketched below 5 4 3 2 f x N 8 7 32 2 14 2 3 4 5 6 7 8 1 2 3 A

3 approave comm 30

Calculate the distance AB AF 7 80mts DA 7 00mts DF 4 00mts DE 15 00mts EB 8 00mts 100 58 0 A 0

Solve for x in the triangle Round your answer to the nearest tenth 36 11

ometry A boy flying his kite releases the entire length of his string which measures 42 m so that the kite is 19 meters above him If the an the string makes with the horizontal ground is find 0 to two decimal places 42 m 19 m 9

In a right triangle ZA and ZB and are acute If sin B O 0 533 32 O 0 011 O 0 846 8 15 what is cos B VAN

Find the length of each arc Round to the nearest tenth 5T 3 5 62 4 6 units O 44 1 units

A CAP and ARAD are two right angled triangles CAP ZARD Find the length of CR R O 20 O23 O 13 17 8 A P D 15 C

The graph below represents the function as a transformation of its parent func y 2 x 2 2 20 2 Select one True False radium sample to

The crew of a helicopter need to land temporarily in a forest and spot a flat horizontal piece of ground a clearing in the forest as a potential landing site but are uncertain whether it is wide enough They make two measurements from A see picture finding a 24 and 53 They rise vertically 100 feet to B and measure y 47 Determine the width of the clearing to the nearest foot ft 184 T HH 100 feet B Y B Ch E clearing

The graph to the right is a function of the form y A sin Bx C D B 0 The five quarter points of one cycle of the graph from left to right are given below These five quarter points on the graph correspond to the five quarter points on the graph of y sin x over the interval 0 2 Determine the equation of the specific function that is represented by the given graph based on the association of the labeled quarter points and the quarter points of the graph of y sin x over the interval 0 2 The quarter points are 3 1 2 2 7 2 4 4 1 3 and 5 4 5 2

Find the value of x 47 58 X

Calculate the following on your calculator Round to the nearest tenth a sin 1 b tan 1 2 sing c C cos 1 d tan 0 2 lo lls bail d 2

5 Ron and Francine are building a ramp for performing skateboard stunts as shown in the accompanying diagram The ramp is 7 feet long and 3 feet high What is the measure of the angle x that the ramp makes with the ground to the nearest tenth of a degree

Determine the value of FG and FH to the nearest tenth There may be multiple possible methods but final ers should be the same G F 60 10 H

6 In right triangle ABC below mzC 28 4 and AC 15 Determine the perimeter of AABC

14 YB 6x 9 YA 5x 2 Find x Then find YA 15 DA 2x 1 DZ 4x 10 Find x Find DA Y X A B

In ATUV Y is the centroid 8 If YW 9 find TY and TW 9 If YU 9 find ZY and ZU 10 If VX 9 find VY and YX T X U Z W V

16 In triangle ABC the measure of angle C is 90 If SinA What is Cos B A 3 2 co or Alor B 1 12 C 2 12 D 1 1

If the average arithmetic mean of 3x and 11 is a the of 4x and 6 is b and the average of 5x and 7 is average C what is the average of a b and c in terms of x A x 2 B x 3 C 2x 4 D 4x 8

6 In the diagram below of right triangle t is the hypotenuse If 0 46 and t etermine s and r to the nearest whole number r

1 Kationalize the denominator 4 2 12 2 J LW 2 2 3 4 Multiply 4 2 x 2 2 3 4 3

3 7 1 8 Solve for the missing side length If using Pythagorean Theorem Pound your answers to the nearest 100th If the triangle can be solved using a special right triangle Patio leave answer as a simplified Radical X D 14 60 X 30 X 8 17 8 X 20 2 4 8 12 45 X 3 2 X X 8 D 30 45 9 10